Answer :
Final answer:
The result of the division x^4 + 6x^3 - 4x^2 - 16x - 7 by x + 1 is x^3 + 5x^2 - 9x - 16. This conclusion is reached by using the synthetic division method.
Explanation:
To find the result when x^4 + 6x^3 - 4x^2 - 16x - 7 is divided by x + 1, we can use polynomial division or synthetic division method. For this situation, let's use synthetic division, and remember that the coefficients of the dividend are 1, 6, -4, -16 and -7.
Step 1: Write down those coefficients in the top row. Step 2: The root that corresponds to the divisor x+1 is -1 so write -1 down in the lower left corner. Step 3: Now, perform synthetic division: Carry down the initial coefficient (1), and multiply with -1, which is written under the next coefficient. Repeat this process across the row. The bottom row now represents the coefficients of the result polynomial (the quotient).
So, the result when x^4 + 6x^3 - 4x^2 - 16x - 7 is divided by x + 1 is x^3 + 5x^2 - 9x - 16, so the correct answer is b.
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